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arXiv · 2012.08614

Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials

John Acosta·Cezary Gonera
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Abstract

A Hamiltonian dynamics defined on the two-dimensional hyperbolic plane by coupling the Morse and Rosen-Morse potentials is analyzed. It is demonstrated that orbits of all bounded motions are closed iff the product of the parameter $\tilde a$ of the Morse potential and the square root of the absolute value of the curvature is a rational number. This property of trajectories equivalent to the maximal superintegrability is confirmed by explicit construction of polynomial superconstant of motion.

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John Acosta, Cezary Gonera. 2020-12-15. Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials. https://arxiv.org/abs/2012.08614

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